Using a set of injections, we include those which pass a detection threshold in the summation over the found injections. For the injections provided in [1]}, we use a threshold of FAR \(<\)  1 yr\(^{-1}\) , consistent with the choice made in [2]}. We do not run the detection pipelines to assign a FAR to each of the injections from our custom injection set in this paper, so we threshold these on an optimal SNR \(>\)  10. Since importance sampling Monte Carlo integration relies on drawing enough samples from the fiducial distribution that cover the support of the target distribution, using Eq. REF  as a reliable estimator for Eq. REF  requires a suitable number of “found” injections to get a well-converged estimate (i.e. see [3]}). With too few samples being used to compute the Monte Carlo approximation, the resulting estimate may be a poor approximation and associated with a high statistical variance (uncertainty), leading to a biased value of the log likelihood.
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